14 – 5 Dilations.

1 / 9

# 14 – 5 Dilations. - PowerPoint PPT Presentation

14 – 5 Dilations. Center Scale factor. A dilation D O, k maps any point P to a point P`, determined as follows: 1) If k > 0, P` lies on OP and OP` = |k|OP 2) If k<0, P` lies on the ray opposite OP and OP` = |K|OP 3) The center is its own image. P. O.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## 14 – 5 Dilations.

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
1. 14 – 5 Dilations. Center Scale factor A dilation DO, k maps any point P to a point P`, determined as follows: 1) If k > 0, P` lies on OP and OP` = |k|OP 2) If k<0, P` lies on the ray opposite OP and OP` = |K|OP 3) The center is its own image P O |k| > 1 is an EXPANSION, expands the picture |k| < 1 is a CONTRACTION, shrinks the picture

2. A dilation DO, k maps any point P to a point P`, determined as follows: 1) If k > 0, P` lies on OP and OP` = |k|OP 2) If k<0, P` lies on the ray opposite OP and OP` = |K|OP 3) The center is its own image B` B A` C` A C O 1) Draw a line through Center and vertex. 2) Extend or shrink segment by scale factor. (Technically by construction and common sense) 3) Repeat, then connect. |k| > 1 is an EXPANSION, expands the picture |k| < 1 is a CONTRACTION, shrinks the picture

3. A dilation DO, k maps any point P to a point P`, determined as follows: 1) If k > 0, P` lies on OP and OP` = |k|OP 2) If k<0, P` lies on the ray opposite OP and OP` = |K|OP 3) The center is its own image B A B` C A` C` |k| > 1 is an EXPANSION, expands the picture |k| < 1 is a CONTRACTION, shrinks the picture O

4. A dilation DO, k maps any point P to a point P`, determined as follows: 1) If k > 0, P` lies on OP and OP` = |k|OP 2) If k<0, P` lies on the ray opposite OP and OP` = |K|OP 3) The center is its own image B A C C` O A` |k| > 1 is an EXPANSION, expands the picture |k| < 1 is a CONTRACTION, shrinks the picture B` If you notice, a negative k in a way rotates the picture

5. Theorem 14 – 5: A dilation maps any triangle to a similar triangle. Cor 1: A dilation maps an angle to a congruent angle. Cor 2: A dilation Do,k maps any segment to a parallel segment |k| times as long Cor 3: A dilation Do,k maps any polygon whose area is k2 times as large. Let’s discuss some justification here, types of invariancy.

6. B B O A A C O C

7. Remember, different slides for different periods. • F - HW #70: Pg 590: 31, 32, 34, 35, 36. Pg 596: 6—14 even, 15—19, 22, 23, 25, 26